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5 votes
2 answers
557 views

What is the proper name for this "tersest path" problem in Infinite Craft?

The web game Infinite Craft gives you a starting set of elements $V_0\subset V$ and a mapping $E$ of type $V\times V\rightarrow V$. In fact, $F$ is commutative: $E(v_a,v_b) = E(v_b,v_a)$. So another ...
1 vote
0 answers
35 views

Term or reference for a set of integer edge weights to guarantee distinct weighted degrees

I am looking for a term or reference describing sets $S$ of $\binom{n}{2}$ non-negative integers such that, for every bijection $w: E(K_n)\to S$ and every pair of distinct vertices $u$ and $v$ in $V(...
1 vote
0 answers
33 views

Name for a Lower Bound on the Length of General TSPs and ATSPs

Let $G\left(\ V,\ E=V\times V\setminus\lbrace(v_i,v_i)\rbrace,\ \Omega: E\ni e_{ij}\mapsto\omega_{ij}\in\mathbb{R}\right)$ be a(n) (A)TSP instance. Then $$2*\ell(T_{\mathrm{opt}})\quad\ge\quad\sum_{v\...